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# Digital image processing unit 1

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• 1. www.jntuworld.com LCE/7.5.1/RC 01 TEACHING NOTES Department: ELECTRONICS & COMMUNICATION ENGINEERING Unit: II Date: Topic name: Retarded Potential No. of marks allotted by JNTUK: Books referred: 01. Antennas for All Applications by John D. Kraus & Ronald J. Marhefka 02. Antenna & Wave Propagation by K. D. Prasad 03. www.wikipedia.org Retarded Potential: The retarded potential formulae describe the scalar or vector potential for electromagnetic fields of a time-varying current or charge distribution. The retardation between cause and effect is thereby essential; e.g. the signal takes a finite time, corresponding to the velocity of light, to propagate from the source point r’ of the field to the point r, where an effect is produced or measured. Otherwise, the formulas below correspond to the same superposition principle acting, e.g., in electrostatics for Coulombs law. These are the electromagnetic retarded potentials for an arbitrary source in free space (vacuum). They satisfy the inhomogeneous wave equations for Φ and A in the Lorenz gauge. Here, r is location, t is time, and is the speed of light in a vacuum. tr is the "retarded time"; the time at which light must be emitted from location r’ in order to reach location r at time t. ρ (r,t) is the electric charge density, and J (r,t) is the current density. ε0 is the dielectric constant of free space and μ0 is the magnetic permeability of free space. ф (r,t) is the electrical potential, and A (r,t) is the vector potential. Finally, dτ’ is the integration measure corresponding to r’. From ф (r,t) and A (r,t) the electromagnetic fields E (r,t) and B (r,t) can be calculated, The corresponding advanced potentials, essentially mathematical objects, are: Faculty/Date: HOD/Date: Page 1 of 11